What type of wave is comprised of sine waves at the fundamental frequency and all its harmonics?

The correct answer is the sawtooth wave, which is characterized by being composed of a fundamental frequency along with all of its harmonics.

A sawtooth wave is defined as a non-sinusoidal waveform that ramps upwards and then sharply drops back, creating a shape that resembles the teeth of a saw. In terms of its harmonic content, a sawtooth wave contains not just the fundamental frequency, but also all integer multiples of that frequency, which means it includes all harmonics. This characteristic makes the sawtooth wave rich in tonal qualities and valuable for applications in audio synthesis and signal processing.

In contrast, other waveforms like square and triangle waves have more limited harmonic content. A square wave consists of the fundamental frequency and only odd harmonics, while a triangle wave contains the fundamental frequency and odd harmonics as well, but with each harmonic dropping off in amplitude much more rapidly than in a sawtooth wave. Sine waves, on the other hand, contain only the fundamental frequency with no harmonics present. This distinction in harmonic composition is key to understanding why the sawtooth wave is the correct answer in this context.